The invention is related to a device for Connection Admission Control (CAC) for an ATM switch, intended for admitting to said ATM swich an additional traffic stream, via an additional ATM connection of the DBR type, such that the “Quality of Service” of all DBR connections in said switch continues to meet certain conditions, a single buffer with capacity B being available for the composite traffic stream of all DBR connections at an output port with capacity C, while, as boundary condition, the total average load of the output port does not amount to more than ρ×C, where ρ is a constant with a value between 0 and 1.